提出了随机脉冲随机微分方程模型, 其中所谓的随机脉冲是指脉冲幅度由随机变量序列驱动,并且脉冲发生的时间也是 一个随机变量序列. 因此, 随机脉冲随机微分方程是对带跳的随机微分方程模型的推广. 利用Gronwall不等式、 Lipschtiz条件和随机分析技巧, 得到了随机脉冲随机微分方程的解的存在唯一性条件.

In the paper, stochastic differential equations with random impulses is first brought forward, where the so-called random impulses mean that impulse ranges are driven by some stochastic sequence and impulse times are a sequence of random variables, so these equations extend stochastic differential equations with jumps. Then existence and uniqueness of solutions to such equations are discussed by employing the Gronwall inequality, Lipschtiz condition, and some techniques in stochastic analysis.